We should note that the initialization choice Eq. (REF ) (e.g. the creation of the Dicke state \(|\psi _0\rangle \) , which requires in principle \(\mathcal {O}(\kappa N)\)  gates [1]}), while being the simplest to analyze and possibly the most advantageous based in prior studies of similar problems [2]}, might be impractical in the near-term. As discussed in [3]}, [4]}, the initialization procedure could be possibly substituted by a simpler to realize superposition of feasible states or a classical warm start candidate followed by a mixing round in QAOA. In QAMPA, the first logical layer contains mixing so initialization might come for free if the gate is appropriately synthesized. Hence, initialization is not a concern for the discussion around compilation efficiency.
